Original title for the thread, Navi
Apart from the presence of the influence, my impression is that those tenses define the time of writing.
In (1), the person may not write any more. When (s)he wrote, (s)he was influenced by the work of Kafka.
In (3), the person started to write at some time in the past and continues to do so, always under the influence of that author. (S)He has been a writer for some time.
My problem with '2' is that to me it implies that I am still being influenced by Kafka. But even if the influence is still there, I am not being influenced by him, or am I?
I am a bit confused!
I'm not sure I understand the reason for your confusion. To me, (2) only expresses that the person is currently writing and under the influence of Kafka while doing so. (S)He may have become a writer recently, or been a writer for some time. One thing is certain: reference is being made to the current influence of Kafka's work on his/her own work.